Question

geometry: algebra review packet
part 3: solving equations
solve each equation.

1. ( y - 5 = 3 )
2. ( 9 = t + 9 )
3. ( 63 + x = 90 )
4. ( y + 42 = 180 )
5. ( \frac{x}{3} = -9 )
6. ( -9p = -45 )
7. ( -4 + 7x = 3 )
8. ( 9 = 6 - (x + 2) )
9. ( 6x + 3 - 8x = 13 )
10. ( 4(x - 2) + 2x = 40 )
11. ( 2x + 7 + 30 + 63 = 180 )
12. ( t + t + 115 = 180 )
13. ( 5x - 6 = 2x - 4 )
14. ( 7x - 4 + 36 = 4x + 47 )
15. ( 4x - 1 + 2x + 1 = 8x - 4 )
16. ( g + 18 = 6g - 2 )
17. ( 3x + 9 + 5x + 9 = 90 )
18. ( 3x - 14 = 2x + 10 )
19. ( 2x + 5x + 5 = 180 )
20. ( x + 27 = 3x - 27 )
21. ( 48 = 2(7x - 1) )
22. ( x + 5 = 3y ) (note: the original ocr for this might have some handwriting issues, but the equation is approximated as such)
23. ( 2(x - 4) = 10 ) (note: the original ocr for this might have some handwriting issues, but the equation is approximated as such)
24. ( 24 = 2(x - 6) )

Explanation:

Step1: Isolate $y$ by adding 5

$y - 5 + 5 = 3 + 5$

Step2: Simplify to find $y$

$y = 8$

Step1: Isolate $t$ by subtracting 9

$9 - 9 = t + 9 - 9$

Step2: Simplify to find $t$

$t = 0$

Step1: Isolate $x$ by subtracting 63

$63 + x - 63 = 90 - 63$

Step2: Simplify to find $x$

$x = 27$

Step1: Isolate $y$ by subtracting 42

$y + 42 - 42 = 180 - 42$

Step2: Simplify to find $y$

$y = 138$

Step1: Isolate $z$ by multiplying by 3

$\frac{z}{3} \times 3 = -9 \times 3$

Step2: Simplify to find $z$

$z = -27$

Step1: Isolate $p$ by dividing by -9

$\frac{-9p}{-9} = \frac{-45}{-9}$

Step2: Simplify to find $p$

$p = 5$

Step1: Isolate $7x$ by adding 4

$-4 + 7x + 4 = 3 + 4$

Step2: Simplify to get $7x=7$

$7x = 7$

Step3: Solve for $x$ by dividing by 7

$\frac{7x}{7} = \frac{7}{7}$

Step4: Simplify to find $x$

$x = 1$

Step1: Distribute the negative sign

$9 = 6 - x - 2$

Step2: Combine like terms

$9 = 4 - x$

Step3: Isolate $-x$ by subtracting 4

$9 - 4 = 4 - x - 4$

Step4: Simplify to get $5=-x$

$5 = -x$

Step5: Multiply by -1 to find $x$

$x = -5$

Step1: Combine like terms

$-2x + 3 = 13$

Step2: Isolate $-2x$ by subtracting 3

$-2x + 3 - 3 = 13 - 3$

Step3: Simplify to get $-2x=10$

$-2x = 10$

Step4: Solve for $x$ by dividing by -2

$\frac{-2x}{-2} = \frac{10}{-2}$

Step5: Simplify to find $x$

$x = -5$

Step1: Distribute the 4

$4x - 8 + 2x = 40$

Step2: Combine like terms

$6x - 8 = 40$

Step3: Isolate $6x$ by adding 8

$6x - 8 + 8 = 40 + 8$

Step4: Simplify to get $6x=48$

$6x = 48$

Step5: Solve for $x$ by dividing by 6

$\frac{6x}{6} = \frac{48}{6}$

Step6: Simplify to find $x$

$x = 8$

Step1: Combine constant terms

$2x + 100 = 180$

Step2: Isolate $2x$ by subtracting 100

$2x + 100 - 100 = 180 - 100$

Step3: Simplify to get $2x=80$

$2x = 80$

Step4: Solve for $x$ by dividing by 2

$\frac{2x}{2} = \frac{80}{2}$

Step5: Simplify to find $x$

$x = 40$

Step1: Combine like terms

$2t + 115 = 180$

Step2: Isolate $2t$ by subtracting 115

$2t + 115 - 115 = 180 - 115$

Step3: Simplify to get $2t=65$

$2t = 65$

Step4: Solve for $t$ by dividing by 2

$\frac{2t}{2} = \frac{65}{2}$

Step5: Simplify to find $t$

$t = 32.5$

Step1: Isolate $3x$ by subtracting $2x$

$5x - 2x - 6 = -4$

Step2: Simplify to get $3x-6=-4$

$3x - 6 = -4$

Step3: Isolate $3x$ by adding 6

$3x - 6 + 6 = -4 + 6$

Step4: Simplify to get $3x=2$

$3x = 2$

Step5: Solve for $x$ by dividing by 3

$\frac{3x}{3} = \frac{2}{3}$

Step6: Simplify to find $x$

$x = \frac{2}{3}$

Step1: Combine constant terms

$7x + 32 = 4x + 47$

Step2: Isolate $3x$ by subtracting $4x$

$7x - 4x + 32 = 47$

Step3: Simplify to get $3x+32=47$

$3x + 32 = 47$

Step4: Isolate $3x$ by subtracting 32

$3x + 32 - 32 = 47 - 32$

Step5: Simplify to get $3x=15$

$3x = 15$

Step6: Solve for $x$ by dividing by 3

$\frac{3x}{3} = \frac{15}{3}$

Step7: Simplify to find $x$

$x = 5$

Step1: Combine like terms

$6x = 8x - 4$

Step2: Isolate $-2x$ by subtracting $8x$

$6x - 8x = -4$

Step3: Simplify to get $-2x=-4$

$-2x = -4$

Step4: Solve for $x$ by dividing by -2

$\frac{-2x}{-2} = \frac{-4}{-2}$

Step5: Simplify to find $x$

$x = 2$

Step1: Isolate $2g$ by subtracting $6g$

$g - 6g + 18 = -2$

Step2: Simplify to get $-5g+18=-2$

$-5g + 18 = -2$

Step3: Isolate $-5g$ by subtracting 18

$-5g + 18 - 18 = -2 - 18$

Step4: Simplify to get $-5g=-20$

$-5g = -20$

Step5: Solve for $g$ by dividing by -5

$\frac{-5g}{-5} = \frac{-20}{-5}$

Step6: Simplify to find $g$

$g = 4$

Step1: Combine like terms

$8x + 18 = 90$

Step2: Isolate $8x$ by subtracting 18

$8x + 18 - 18 = 90 - 18$

Step3: Simplify to get $8x=72$

$8x = 72$

Step4: Solve for $x$ by dividing by 8

$\frac{8x}{8} = \frac{72}{8}$

Step5: Simplify to find $x$

$x = 9$

Step1: Isolate $x$ by subtracting $2x$

$3x - 2x - 14 = 10$

Step2: Simplify to get $x-14=10$

$x - 14 = 10$

Step3: Isolate $x$ by adding 14

$x - 14 + 14 = 10 + 14$

Step4: Simplify to find $x$

$x = 24$

Step1: Combine like terms

$7x + 5 = 180$

Step2: Isolate $7x$ by subtracting 5

$7x + 5 - 5 = 180 - 5$

Step3: Simplify to get $7x=175$

$7x = 175$

Step4: Solve for $x$ by dividing by 7

$\frac{7x}{7} = \frac{175}{7}$

Step5: Simplify to find $x$

$x = 25$

Step1: Isolate $-2x$ by subtracting $x$

$x - x + 27 = 3x - x - 27$

Step2: Simplify to get $27=2x-27$

$27 = 2x - 27$

Step3: Isolate $2x$ by adding 27

$27 + 27 = 2x - 27 + 27$

Step4: Simplify to get $54=2x$

$54 = 2x$

Step5: Solve for $x$ by dividing by 2

$\frac{2x}{2} = \frac{54}{2}$

Step6: Simplify to find $x$

$x = 27$

Step1: Distribute the 2

$48 = 14x - 2$

Step2: Isolate $14x$ by adding 2

$48 + 2 = 14x - 2 + 2$

Step3: Simplify to get $50=14x$

$50 = 14x$

Step4: Solve for $x$ by dividing by 14

$\frac{14x}{14} = \frac{50}{14}$

Step5: Simplify to find $x$

$x = \frac{25}{7}$

Step1: Isolate $-2y$ by subtracting $3y$

$y - 3y + 5 = 0$

Step2: Simplify to get $-2y+5=0$

$-2y + 5 = 0$

Step3: Isolate $-2y$ by subtracting 5

$-2y + 5 - 5 = 0 - 5$

Step4: Simplify to get $-2y=-5$

$-2y = -5$

Step5: Solve for $y$ by dividing by -2

$\frac{-2y}{-2} = \frac{-5}{-2}$

Step6: Simplify to find $y$

$y = 2.5$

Step1: Distribute the 2

$2x - 8 = 10$

Step2: Isolate $2x$ by adding 8

$2x - 8 + 8 = 10 + 8$

Step3: Simplify to get $2x=18$

$2x = 18$

Step4: Solve for $x$ by dividing by 2

$\frac{2x}{2} = \frac{18}{2}$

Step5: Simplify to find $x$

$x = 9$

Step1: Distribute the 2

$24 = 2x - 12$

Step2: Isolate $2x$ by adding 12

$24 + 12 = 2x - 12 + 12$

Step3: Simplify to get $36=2x$

$36 = 2x$

Step4: Solve for $x$ by dividing by 2

$\frac{2x}{2} = \frac{36}{2}$

Step5: Simplify to find $x$

$x = 18$

Answer:

1. $y=8$
2. $t=0$
3. $x=27$
4. $y=138$
5. $z=-27$
6. $p=5$
7. $x=1$
8. $x=-5$
9. $x=-5$
10. $x=8$
11. $x=40$
12. $t=32.5$
13. $x=\frac{2}{3}$
14. $x=5$
15. $x=2$
16. $g=4$
17. $x=9$
18. $x=24$
19. $x=25$
20. $x=27$
21. $x=\frac{25}{7}$
22. $y=2.5$
23. $x=9$
24. $x=18$